When talking about Priest’s “Combo” people usually mean the combo pretty much as old as the game itself – Divine Spirit + Inner Fire. Some iterations of the deck appear in nearly every meta. They can be stronger or weaker depending on the support, the general play style and card choices might also change, but overall it’s one of the most powerful strategies available to Priests in general.
In Saviors of Uldum, Combo Priest is more of an Aggro/Tempo deck supplemented by the combo. With a low curve, great cycling and powerful early game plays, the goal is to develop the board, protect it, keep it healthy and then play Divine Spirit + Inner Fire on your highest Health minion. Most of the time you aren’t directly killing your opponent, but rather making a huge threat (like a 12/12 minion) that is out of the removal range of your opponent. Additions of cards like High Priest Amet, Injured Tol'vir, Neferset Ritualist or Psychopomp pushed the deck straight into Tier 1. In fact, the deck is so good that one of the cards was already nerfed (Extra Arms: 2 -> 3 mana) and there’s no telling whether we won’t see another nerf to address the deck’s strength.